论文标题
三个差距定理和周期函数
The Three Gap Theorem and Periodic Functions
论文作者
论文摘要
三个差距定理，也称为斯坦豪斯的猜想，是分数零件函数组合的经典结果，此后已通过许多方式进行了概括。在本文中，我们提出了一个与这些结果相关的新问题：三个差距定理的其他周期函数都具有哪些周期性功能？我们证明了某些类别线性周期函数的某些类别的结果，并证明了在间隙长度数量上没有结合的函数的存在。
The Three Gap Theorem, also known as the Steinhaus Conjecture, is a classical result on the combinatorics of the fractional part function, and has since been generalized in many ways. In this paper, we pose a new problem related to these results: for which other periodic functions does an analogue of the Three Gap Theorem hold? We prove analogous results for certain classes of piecewise-linear periodic functions and demonstrate the existence of functions for which no bound exists on the number of gap lengths.
